Displaying similar documents to “Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements”

Approximations of the partial derivatives by averaging

Josef Dalík (2012)

Open Mathematics

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A straightforward generalization of a classical method of averaging is presented and its essential characteristics are discussed. The method constructs high-order approximations of the l-th partial derivatives of smooth functions u in inner vertices a of conformal simplicial triangulations T of bounded polytopic domains in ℝd for arbitrary d ≥ 2. For any k ≥ l ≥ 1, it uses the interpolants of u in the polynomial Lagrange finite element spaces of degree k on the simplices with vertex...

Boundary of the union of rectangles in the plane

Václav Medek (1983)

Aplikace matematiky

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Given n rectangles in a plane whose all sides belong to two perpendicular directions, an algorithm for the construction of the boundary of the union of those rectangles is shown in teh paper.

How to recover the gradient of linear elements on nonuniform triangulations

Ivan Hlaváček, Michal Křížek, Vladislav Pištora (1996)

Applications of Mathematics

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We propose and examine a simple averaging formula for the gradient of linear finite elements in R d whose interpolation order in the L q -norm is 𝒪 ( h 2 ) for d < 2 q and nonuniform triangulations. For elliptic problems in R 2 we derive an interior superconvergence for the averaged gradient over quasiuniform triangulations. A numerical example is presented.